Complex numbers corresponding to four vertices of square are roots of the equation  x^4 + bx^3 +cx^2+dx+e=0 with integer coeficients find the minimum area of the square

problem on conic sections-1

A(0,2) ,B and C are three points on the parabolaY^2 = x + 4  such that AB is perpendicular to BC  find the range of values of  y

Problem on Triangle(2)

ABC is an equilateral  triangle let point P be inside triangle let D , E , F be feet of perpendiculars from P upon BC , CA, AB respectively  Show that PD+PE+PF is independent of choice of P